Gaming devices, such as slot machines, having primary and secondary or bonus games or schemes are well known. One well known bonus game provides a player with a series of award offers consisting of credits or dollars. The player may either accept each award offer or reject each award offer; however, the player must accept the final award offer. If the player accepts an award offer, the player keeps the award offered. If the player rejects the award offer, the gaming device provides another award offer to the player except if the award offer is the final award offer. The award offers are randomly determined from a series of award offers of differing values. As illustrated in FIG. 3, the potential award offers 52 are displayed to the player, each award offer made by the game is displayed in an offer display 54, the number of offers remaining are displayed in an offer remaining display 56, and accept and reject buttons 58 and 60, respectively, enable the user to accept or reject the offers.
Several different embodiments of this type of bonus scheme for a gaming device have been implemented in gaming machines of various types. While this type of gaming device has achieved significant popularity in the gaming industry, after playing the game repeatedly, players may lose interest in the game. Accordingly, there is a need for new gaming devices related to this type of offer and acceptance bonus scheme.